非齐次线性微分方程的有限级解

详细信息

Finite order solutions of non-homogeneous linear differential equations with entire coefficients

摘要: 研究了非齐次线性微分方程 $f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_1(z)f'+A_0(z)f=F(z)$ 有限级解的增长性,其中 $A_j(z)\hspace{0.2cm}(j=0,\cdots,k-1)$ 和 $F(z)$ 都是整函数,并且存在某个 $A_s(z)$ 在某个扇形内以指数的形式起支配作用.
- 微分方程 /
- 有限级 /
- 整函数
Abstract: The growth of finite order solutions of non-homogeneous linear differential equation $f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_1(z)f'+A_0(z)f=F(z)$ is considered, where $A_j(z),~j=0,\cdots,k-1,~F(z)$ are entire functions,and there exists some $A_s(z)$ as exponentially dominating in a sector.
- differential equations /
- finite order /
- entire function